1. Field of the Invention
The present invention relates to an image-formation optical system used in optical apparatuses, such as image projection apparatuses or image-taking apparatuses.
2. Description of Related Art
In recent years, in order to enlarge and display images created with a computer, image projection apparatuses, such as front projection-type projectors (front projectors), have come to be widely used. In such image projection apparatuses, smaller size and lighter weight is of course desired, and they often use projection optical systems which can project obliquely onto a screen in order to perform image projection without obstructing the visual field of the observer. Since with oblique projection the image projected onto the screen is distorted by so-called trapezoidal distortion, methods for correcting this trapezoidal distortion have been proposed for example in Japanese Patent Application Laid Open No. H10 (1998)-282451.
On the other hand, regarding non-coaxial optical systems, Japanese Patent Application Laid Open No. H09, (1997)-5650 discloses a method for designing a non-coaxial optical system and a method for calculating paraxial quantities such as the focal length, and Japanese Patent Application Laid Open No. H08 (1996)-292371, Japanese Patent Application Laid Open No. H08 (1996)-292372, and Japanese Patent Application Laid Open No. H09 (1997)-222561 disclose design examples for non-coaxial optical systems. In these documents, the concept of the “reference axis” is introduced, and they clarify that it is possible to construct an optical system with sufficiently corrected aberrations by making the constituent surfaces of the optical system aspherical surfaces which are asymmetrically shaped with respect to the reference axis.
Such a non-coaxial optical system is also referred to as an off-axial optical system, and, when the path which a light ray passing through the image center and the pupil center is taken as the reference axis, it is defined as an optical system including curved surfaces whose surface normals on the intersection between the surface and the reference axis do not coincide with the reference axis (off-axial curved surfaces). In this case, the reference axis has a bent shape.
The constituent surfaces of such an off-axial optical system are ordinarily non-coaxial, and it is easy to construct the optical system using reflective surfaces, since no vignetting occurs at the reflective surfaces. Moreover, by forming an intermediate image within the optical system, it is possible to configure a compact optical system while ensuring a large field angle.
Furthermore, it is possible to configure a compact optical system in which the optical path can be laid out comparatively freely while arranging the aperture stop in front of the optical system.
In the optical systems proposed in Japanese Patent Application Laid Open No. 2001-255462 (corresponding to U.S. Pat. No. 6,626,541) and Japanese Patent Application Laid Open No. 2000-89227, the strong points of such off-axial optical systems are utilized to correct the trapezoidal distortion at a fixed projection angle by using curved and rotationally asymmetric reflective surfaces.
On the other hand, small size and low profile are also desired for image-taking optical systems used for image-taking apparatuses such as cameras. In Japanese Patent Application Laid Open No. H08 (1996)-292372 described above, a small low-profile zoom image-taking optical system is proposed, which uses curved and rotationally asymmetric reflective surfaces.
However, off-axial optical systems using such reflective surfaces are often very sensitive to manufacturing discrepancies in surface precision or decentering or the like. For example, when there are asymmetric discrepancies in the surface shapes, the focus position deviates across the entire image surface for two directions orthogonal to each other in the image surface, that is, an astigmatic difference occurs. It is difficult to overcome this through mechanical adjustments during manufacturing in practice.